Question

What is the product in simplest form? State any restrictions on the variable. Please help? medal
(x^2+7x+10)/(x+3) * (x^2-3x-18)/(x^2+x-2)

Answer 1

First, factor x²+7x+10, x²-3x-18 and x²+x-2.
Then write as one fraction (multiply numerators, denominators)
Then cancel the common factors of numerator and denominator.
Then: you're done!

Answer 2

E.g. x²+7x+10=(x+2)(x+5), you know, sum of 2 and 5 is 7, product is 10

Answer 3

(of course, you still have to state restrictions...)

Answer 4

im confused...

Answer 5

\[{{x^2+7x+10}\over{x+3}} \times {{x^2-3x-18}\over{x^2+x-2}}\]factor all the polynomials:\[{{(x+5)(x+2)}\over{x+3}} \times {{(x-6)(x+3)}\over{(x+2)(x+1)}}\]cross out what can be cancelled:\[{{(x+5)\cancel{(x+2)}}\over\cancel{{x+3}}} \times {{(x-6)\cancel{(x+3)}}\over{\cancel{(x+2)}(x+1)}}\]this leaves you with:\[{{x+5}\over{1}}\times{{x-6}\over{x+1}}\]multiply straight across:\[{x^2-x-30}\over{x+1}\]
now for the restrictions, those are any binomials that you cross out.
so we crossed out \((x+2)\) and \((x+3)\) so lets solve for those:\[x+2\neq0~~~\implies ~~~x\neq-2\]\[x+3\neq0~~~\implies ~~~x\neq-3\]

so your final answer is \[\large{{x^2-x-30}\over{x+1}}~~~where~~x\neq-2~~and~~x\neq-3\]

hope this helps! :) @whadduptori